What you are looking for is page-attributes support in the post type. However…
‘page-attributes’ (
template andmenu order) (hierarchical must be
true) (the page template selector is only available for the page post
type)
… and posts are not hierarchical. I am not sure you can force them to be, never mind the potential issues with altering a built in post type like that.
Additionally, that ‘order’ values in not used very much by default, and certainly not by “post” post type queries so you’d need to alter a number of queries to get that to work. I think there are hooks enough to do it but it would be a bit of work.
My advise is that if you need another page-like post type, just create one.